Various gaming systems have been developed to facilitate competitive play on reel-type and other games which are traditionally operated in an individual play mode. In an individual play mode the player may make a wager in the game and then activate the game to obtain their individual result. In competitive play, a player or team of players, each at a respective gaming machine may activate the game repeatedly in order to produce a score which is compared to the scores of other players or teams to determine which player or team is the winner of the competition. There continues to be a need for innovative methods and gaming systems which present competitive games in different ways to generate player interest and excitement.